Digital Directional and Non-Directional Over Current Relays: Modelling and Performance Analysis
Digital Directional and Non-Directional Over Current Relays: Modelling and Performance Analysis
Digital Directional and Non-Directional Over Current Relays: Modelling and Performance Analysis
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
a
Ph.D. Scholar University of Malaya, Malaysia and working as a lecturer in the Department of Electrical Engineering, NED
University of Engineering & Technology. Karachi- Pakistan. Ph. +6014-2274960 Email mohsinaman@siswa.um.edu.my.
b
Electrical Engineer, working in Siemens Pakistan Ph. +92 (0)343-3382510, Email qadeer88@hotmail.com
c
Professor & Chairman, Department of Electrical Engineering, NED University of Engineering & Technology, Karachi-
Pakistan. Ph. +92 (0)21-99261261-8, Email saadqazi@neduet.edu.pk
AbstractThis paper describes the design of a digital over current relay (directional and non
directional) and its performance on MATLAB/SIMULINK. Digital over current relays have
advantages over electromechanical relays. Their fast, compact and reliable operation results in
minimum outage of power system in case of fault. The paper also describes various data
conversion steps involved in a digitization process. The logic based algorithm and developed
relay model have been tested under various system dynamics and fault conditions. A 400V
industrial distribution power system is used as a tutorial to simulate and test over-current relays
performance results, with motor start up inrush current consideration and backup relay
coordination for safe and reliable operation. Similarly, a 132kV loop network is used as another
tutorial example to simulate and test the directional over-current relays performance.
Key Words: Digital relay, over current relay, inverse and instantaneous characteristics, slope
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
1. INTRODUCTION
S IMULATION tools are becoming more and more useful in initial designing of power system as a tool
for researcher and in the educational field to give real time feelings to fresh engineers. Currently,
varieties of software tools are available to power engineers such as ETAP, DigSilent and Power World
Simulator (PWS). These tools are useful but need substantial training to use. MATLAB also offers an
open-source Power System Analysis Toolbox for electric power system and control. This toolbox
covers many aspects of power system although it currently does not possess many protection system
components modules [1]. This paper covers the design of a digital over-current relay (OCR) model and
directional OCR on MATLAB/Simulink. Modelling in MATLAB offers design flexibility and room
for exploration which assists in developing better understanding of the physical phenomenon
Any protection scheme is a combination of various types of relays such as Over-current, over and
under-voltage, over and under-frequency relays etc. All of these were traditionally constructed
electromechanically and later in solid-state. Currently, digital relays have replaced both types; being
faster, compact and reliable in operation ensuring minimum power outage in case of fault [2-5].
OCRs are employed to protect distribution and sub-transmission system from the effects of excessive
currents occurring either due to short circuits or overload conditions. It is also used for the protection of
generators, power transformers and electric motors. To limit the extent of damage caused by such faults
to a minimum level; fast, reliable and selective operation of relay are basic demands of any power
system. To meet these expectations, advantages of digital logic, communication, information storage
and processing capabilities of modern microprocessors are employed in digital design [2-5]. OCR has
its limitation in sensing the direction of fault, which is mitigated by adding a directional element along
with it [4]. Directional OCRs are most commonly employed for protecting ring or loop networks [5-7].
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
2. THEORETICAL BACKGROUND
The currenttime characteristic of a typical over-current relay is shown in Fig. 1 [2, 4, 6-7].
In Fig. 1, Curve A-B is the inverse characteristic of the relay and is used to protect apparatus from
excessive currents less than severe short circuit fault levels but large enough, that if allowed to sustain
for a certain period would damage the apparatus it is meant to protect. Moreover, Curve B-C-D is
meant for instantaneous, high speed clearing of severe short circuits (>IS) by reducing the clearing time
to only Ts. This paper presents the design of inverse as well as instantaneous portion of over-current
relay on MATLAB/SIMULINK.
The general form of the inverse time current characteristic of an over-current relay can be given as [3,
5].
K IS
T 1 Ia (1)
I 1
n
a IP
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
Where T is the operating time of the relay ; Ia is the fault current normalized by the pickup current
IC
i.e. I a ; IC is the actual current; IP is the pickup current and IS is the short circuit current. n and
IP
K are constants. n determines the inverse characteristic of the relay and K determines the relative
operating time of the relay by shifting the inverse characteristics curve on vertical axis of Fig. 1.
K
T I P IC I S (2)
I Cn
Any desired relay curve can be obtained by selecting suitable values of n and K [3]. For instantaneous
portion of curve (BCD) of over current relay the relay operation time is given as (3) [6-7]:
T TS IC I S (3)
Over-current relays employed in a system should be coordinated with other relays in such a manner
that if the primary protection fails to operate, then back- up protection should accomplish the task [6-
8].
For a fault F, beyond bus bar B, relay RB should cause its associated circuit breaker C.BB to clear the
fault. If it fails to do so then relay RA, acting as back-up, should actuate its circuit breaker C.BA, to
ensure fault isolation. For correct grading, the time setting of relay RA should always be greater than
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
that of RB by an amount in which RB was supposed to have cleared the fault and this time is usually the
Failure to satisfy (4), irrespective of correct primary protection operation, will result in back-up
protection to always operate and thus lead to a greater disruption of service [6-7].
Fig. 3 shows the general block diagram for implementing a microprocessor based O.C. relay [9].
The Current transformers (C.T) purpose is to produce a scaled down accurate reproduction of the
power system fault current. Protection class C.T. is employed with good accuracy class for
reproduction of fault current for a wide range to avoid cores saturation [6, 9].
The digital signal in the microprocessor is first conditioned from any decaying DC component and
harmonics present in the signal. DC component may cause relay disoperation even when the steady
state AC component of fault is less than the pickup current setting of the relay [10]. Harmonics induced
into the current signal due to non-linear loads in the power system are filtered out to prevent reduced
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
In this paper, the MATLAB environment serves the purpose of a microprocessor and the algorithm
To protect ring or loop networks directional over current relays are commonly employed. The
directional element is added with the over-current relay in order to minimize the outage area [13, 14]. If
non-directional relays are applied to parallel feeders, any fault occurring on any one of the feeders will
result in complete loss of supply to the other end. With this type of system configuration, it is necessary
to apply directional relays at the receiving end and to grade them with the non-directional relays at the
sending end, to ensure correct discriminative operation of the relays during line faults. This is done by
providing directional relays Q1 and Q2 at the other end looking non directional relays P1 and P2, at the
3. RELAY MODELLING
This section gives the basic logic for implementing the inverse current-time characteristic of an O.C.
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
Figure 5. Logic Diagram for implementing the Inverse Current Time characteristics of OCR
After filtering the fundamental component, ac current signal(I) of frequency f entering the relay must
first converted to a representative dc value( peak/r.m.s.) for comparison with the pre-set pick-up
current of relay. By measuring the slope at the zero crossing of the current signal, we get its peak value
I (t ) I C Sin(2ft ) (5)
dI (t )
I C 2fCos (2ft ) (6)
dt
dI (t )
m I C 2f (7)
dt
m
IC (8)
2f
The implementation of measuring Ic given by (8) on SIMULINK is shown in Fig. 6, in which the
peak obtained at each zero crossing is held constant by the sample and hold block until the next zero
crossing. The detail of zero crossing and its detection can be seen in [15].
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
It may be noted that peak detection in time domain is computationally more expensive and time
taken, frequency based methods such as FFT exist [16-18], which could be used for measuring peak
detection. However, for the sake of simplicity of demonstration, elementary methods have been used
here. The zero-crossing technique can be replaced by more sophisticated phasor estimation methods.
The frequency is determined by measuring the time between two consecutive zero crossings (T1 &
T2). This will give half the time period (T) from which frequency is determined as follows:
T
T2 T1 (9)
2
1 1
Frequency (10)
TimePeriod (T ) 2(T2 T1 )
The frequency measuring block implemented on SIMULINK is shown in Fig. 7. Hit Crossing block
is used, which passes the input signal only at its zero crossings to the if block which in turn sends the
value of the ramp signal at that instant to the output. The time duration of generated ramp can be
computed and can be saved to a variable A. This value of A must be subtracted from the time of the
next zero crossing to determine half the time period. This is done by temporarily storing A into another
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
variable B using the Transport Delay block. Now subtracting B from A at any instant will give half
the time period whose value is held by the Sample and Hold block, till the next zero crossing. After
performing the necessary computations, given by (10), on the held value we get the instantaneous
frequency.
The peak value of current (IC) obtained in section 3.1.1 is then compared with the pre-set constant
value of pickup current (IP) setting of the relay using the comparator block which allows IC when IC >
IP. The value of IC is then raised to a suitable power of n to achieve desired relay curve and then
Constant I Cn dt (11)
As long as the current is in excess of IP (pickup current), the integrator output keeps rising until it
becomes equal to the pre-set value of constant K, causing the relay to send a trip signal (0).
If the excess current is temporary; either due to motor starting or any switching action; the rising
integral output is reset to zero when the excess current dies out to below IP, before reaching K by the
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
If the fault current level is constant during permanent fault, the value of I cn will also remain constant
Constant I Cn dt (12)
Constant I Cn t (13)
(13) is the equation of a straight line with slope I cn .So a large magnitude of fault current will result in
a higher rate of rise of the integrator output and thus a smaller time to reach the value of constant K.
This is shown in Fig. 8 for two current levels IC1 and IC2, providing inverse current time characteristic
If the value of IC as determined from slope detection is greater than the pre-set value of severe short
circuit current level IS (IC>IS), the relay sends a 0 (trip command signal) to its associated C.B. after a
fixed delay of TS seconds. Fig. 9 shows the logic for implementing the instantaneous characteristic;
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
The overall digital relay output is the logical multiplication (AND) of instantaneous element and
The OCR relay designed above can be modified to behave also as a directional O.C. relay simply by
incorporating a directional feature with the relay. The directional feature acts as a switch to allow
current to pass to the O.C. relay to take decision only when power flows in a particular direction [19,
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
These directional relays may use the phase angle between the fault current and some reference
quantity (the corresponding voltage, for example) to determine the direction (forward or reverse) of the
fault [14].
If (let) is the angle between current in a phase and voltage on that phase then
Fig. 12a shows that during normal conditions (-90o < < 90o) the overlapping interval between
voltage and current is longer than their non-overlapping interval whereas under reversed power flow
conditions (90o> > 270o) the opposite is true as shown in Fig. 12b.
Figure 12(a) Angle between Voltage and Current Phasors under normal conditions
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
Figure 12(b) Angle between Voltage and Current Phasors under fault conditions
This difference in the overlapping interval under normal and reversed power flow conditions can be
To model the directional element, the current and voltage signals are first converted to a two level
square wave, whose value is 1 for positive values and -1 for negative values of the signals. The 2
level voltage and currents signals are then multiplied, giving an output 1 during the overlapping and
-1 for the non-overlapping interval. The product is then integrated. The upper limit of the integrator is
set to saturate at a value of 0 so that under normal load flow conditions the integral always remains less
than 0.However,under reversed power flow conditions the integral output tends to fall until it reaches
the level below L, in which case the directional elements output switches from 0 to 1. Fig. 13
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
The directional element with an output 1 under abnormal conditions and 0 otherwise, serves as a
switch by multiplying its output with the samples of current, to be sent to the O.C. relay as illustrated in
Fig. 14.
These models of relays (OCR and Directional OCR) have also been contributed to MATLABs
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
To demonstrate performance of the current time characteristics of the relay designed, we consider a
radial network shown in Fig. 2. The load is considered to be a motor, rated 110kW, 400V, 0.885 power
factors whose initial starting current is 4 times the nominal current. The accelerating period of the
motor is 3 seconds.
1. The pickup current setting IP allows the motor to carry continuous full load current (i.e. 179A r.m.s.
or 253 A peak).
2. Severe fault current setting (IS) is more than the initial starting current of the motor (1000A peak).
3. Constant K is such selected that it does not cause false tripping during motor starting and transient
conditions.
The K and Ts setting of RA is kept greater than that of RB for proper relay coordination. The circuit
During the accelerating period the motor current is above the pickup setting of RB causing its integrator
output to rise. At t=3 seconds, when the motor current falls below IP ,the integrator output being below
the K setting of RB is reset. The K value of RB is purposely set above its maximum integrator output
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
We will now consider cases for different fault current levels occurring at t=6 seconds at position F of
Fig. 2.
In this case the integrator output of RB rises until it reaches the value of K (1100) causing the relay RB
to trip the circuit breaker after 3.7 seconds of fault (neglecting CB operating time). This is shown in
Fig. 15a, indicating the fault current and relay performance during the fault. It can be noticed that the
relay RA will take more time (4.7s) due to greater value of K settings.
K 1100
T 3.7 sec
I Cn 560 n
In this case, the relay RB will operate much quicker than the previous case because the current is more
and the relay follows inverse current-time characteristics. The operating time of the relay can also be
found by:
K 1100
T 2.7 sec
I Cn 770 n
Fig. 15b indicating the relay performance during the fault current of 770A, which clearly shows inverse
In this case C.BB fails to open at 8.7 sec as directed by RB. In that case RA acting as backup operates
C.BA to interrupt the fault current at t=9.5 in 3.5seconds after the fault as verified below.
K 1400
T 3.5 sec
I Cn 770 n
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
Fig. 15c indicating the relays performance during the fault current of 770A, the backup protection
In this case the relay RB will operate instantaneously (0.1 sec) in order to minimize extent of damage to
Fig. 15d is indicating the relays instantaneous characteristic performance during the severe fault
current of 1350A.
Case 5: For fault current Ic=1350A (I S(RB) <IC<I S(RA)) with CBB failing to open.
In this case, relay RA will provide the backup protection. However since the level of fault current falls
in the inverse characteristic region of RA, therefore the time taken by it to operate will be given by
K 1400
T 2.13 sec
I C 1350 n
n
However for fault current Ic=2000A (>IS) with CBB failing to open. The relay RA will provide the
backup protection and operate after 0.2 sec of fault, maintaining coordination with relay RB. Fig. 15f
indicating the relays instantaneous characteristic performance during the severe fault current of
2000A.
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
(a) (b)
Figure 15. Relay Performance for for fault current (a) Ic=560A (b) 770 A
(c) (d)
Figure 15. Relay Performance for fault current (c) Ic=770A & CBB failure (d) Ic=1350A
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
(e) (f)
Figure 15. Relay Performance with CBB failure for fault current (e) Ic=1350 and (f) Is=2000A
Table 2 summarizes the operating times of RA and RB for peak levels of fault current as simulated
above.
network shown in Fig. 4, which shows two parallel 220 kV transmission lines feeding a load(L) such
We will now consider cases for different positions of fault occurring in transmission line i.e.
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
To ensure removal of only line F1 for minimum outage; relays Q1 and Q2 are directional O.C. relays,
functioning only when power flows in the direction [22] as indicated in Fig. 4. Relays P1 and P2 are
non-directional O.C. relays .The fault at R which is fed by the supply through paths S.-P1.-R and S-P2-
Q2-Q1-R causes current levels on both feeders to rise. The direction of power flow remains the same as
prior to the fault in relay Q2 and reverse in Q1, therefore relay Q2 remains idle no matter how high the
current flowing through the respective C.T. is, whereas relay Q1 functions to send a trip command to
the its associated C.B. at t=5.35s resulting in the fault current to no longer be fed from path S-P2-Q2-
Q1-R. Non directional O.C. relay P1 will trip its associated C.B. at t=5.8sec., thereby ultimately
removing the faulty feeder from the network resulting in the entire load current to be fed by healthy
feeder F2.
Fig. 16a shows the status of relays at P1, P2, Q1, Q2 and the currents at the positions of these relays
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
In this case, only P2 and Q2 will open for minimum outage, load will be transferred to the healthy line
F1. Fig. 16b shows the status of relays at P1,P2,Q1,Q2 and the currents at the positions of these relays
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
In this case, no relay will operate since the fault is out of reach. Fig. 16c shows the status of relays at
P1,P2,Q1,Q2 and the currents at the positions of these relays for fault occurring on Bus 1.
In this case, only over-current relays P1 and P2 will operate. Fig. 16d shows the status of relays at
P1,P2,Q1,Q2 and the currents at the positions of these relays for fault occurring on Bus 2.
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
Fig. 16(e-g) shows the status of relays at P1,P2,Q1,Q2 and the currents at the positions of these relays
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
Figure 16 (e) Relay status and fault current in case of SLG fault
Figure 16 (f) Relay status and fault current in case of DLG fault
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
CONCLUSION
Models of Digital OCR and Digital Directional OCR have been presented in this paper in
strengthen their Power System Tools. The performance of these models was showcased using suitable
tutorial examples. It is shown that these models offer effective means for explaining the functionality
of OCR and Directional OCR under various operating scenarios. Additionally, the systematic unfolding
style of model development and performance analysis means that this paper could also serves as guide
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NED University Journal of Research. (Vol. VIII No.2 December 2011)
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